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Continuous Quantum Hidden Subgroup Algorithms
, 2003
"... In this paper we show how to construct two continuous variable and one continuous functional quantum hidden subgroup (QHS) algorithms. These are respectively quantum algorithms on the additive group of reals R, the additive group R/Z of the reals R mod 1, i.e., the circle, and the additive group Pat ..."
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Cited by 4 (1 self)
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In this paper we show how to construct two continuous variable and one continuous functional quantum hidden subgroup (QHS) algorithms. These are respectively quantum algorithms on the additive group of reals R, the additive group R/Z of the reals R mod 1, i.e., the circle, and the additive group Paths of L 2 paths x: [0, 1] → R n in real nspace R n. Also included is a curious discrete QHS algorithm which is dual to Shor’s algorithm. Contents 1
Geometry of abstraction in quantum computation
"... Quantum algorithms are sequences of abstract operations, performed on nonexistent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction i ..."
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Cited by 2 (2 self)
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Quantum algorithms are sequences of abstract operations, performed on nonexistent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction in quantum computation, which turns out to characterize its classical interfaces. Some quantum algorithms provide feasible solutions of important hard problems, such as factoring and discrete log (which are the building blocks of modern cryptography). It is of a great practical interest to precisely characterize the computational resources needed to execute such quantum algorithms. There are many ideas how to build a quantum computer. Can we prove some necessary conditions? Categorical semantics help with such questions. We show how to implement an important family of quantum algorithms using just abelian groups and relations.
ABSTRACT SIMULATING QUANTUM COMPUTING: QUANTUM EXPRESS
"... Quantum Computing (QC) research has gained a lot of momentum recently due to several theoretical analyses that indicate that QC is significantly more efficient at solving certain classes of problems than classical computing. While experimental validation will ultimately be required, the primitive na ..."
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Quantum Computing (QC) research has gained a lot of momentum recently due to several theoretical analyses that indicate that QC is significantly more efficient at solving certain classes of problems than classical computing. While experimental validation will ultimately be required, the primitive nature of current QC hardware leaves practical testing limited to trivial examples. Thus, a robust simulator is needed to study complex QC issues. Most QC simulators model ideal operations, and thus cannot predict the actual time required to execute an algorithm or quantify the effects of errors in the calculation. We have developed a novel QC simulator that models physical hardware implementations. This simulator not only allows the accurate simulation of quantum algorithms on various hardware implementations, but also takes an important step towards providing a framework to determine their true performance and vulnerability to errors. 1
A Survey and Review of the Current StateoftheArt in Quantum Computer Programming
, 2007
"... Quantum computer programming is a new discipline emerging from interdisciplinary research in quantum computing (and several related subdisciplines including quantum information theory, mathematical physics, and measurement theory), computer science, mathematics (especially quantum logic and linear l ..."
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Quantum computer programming is a new discipline emerging from interdisciplinary research in quantum computing (and several related subdisciplines including quantum information theory, mathematical physics, and measurement theory), computer science, mathematics (especially quantum logic and linear logic), and engineering attempts to
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, 2008
"... Algebraically connecting the hardware/software boundary using a uniform approach to highperformance computation for software and hardware applications ..."
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Algebraically connecting the hardware/software boundary using a uniform approach to highperformance computation for software and hardware applications